Question 931472
the line passing through the point O(7,-3) and perpendicular for the line {{{2x-5y=8}}}

{{{y=(2/5)x-8/5}}} => slope is {{{(2/5)}}} and y-intercept is {{{b=-8/5}}}


perpendicular line should have a slope negative reciprocal of {{{(2/5)}}} which is {{{-1/(2/5)=-5/2}}}

then your equation is: {{{y=-(5/2)x+b}}}
use given point to find {{{b}}}

{{{-3=-(5/2)7+b}}}

{{{-3+(5/2)7=b}}}

{{{-6/2+35/2=b}}}

{{{29/2=b}}}


{{{y=-(5/2)x+29/2}}}

{{{ graph( 600, 600, -20, 20, -10, 20, (2/5)x-8/5, -(5/2)x+29/2) }}}